In how many ways can 6 boys form a ring ?

Options

A. 120
B. 720
C. 119
D. none of (a), (b) ,(c )

Answer

To find the number of ways 6 boys can form a ring, we can use the formula for arranging n objects in a circular manner, which is given by (n-1)!. Here’s the step-by-step solution:

### Step 1: Identify the number of boys
We have 6 boys.

### Step 2: Apply the formula for circular permutations
The formula for the number of ways to arrange n objects in a circle is (n-1)!.

### Step 3: Substitute the value of n
In this case, n = 6. Therefore, we calculate (6-1)! = 5!.

### Step 4: Calculate 5!
Now, we need to calculate 5! (5 factorial):
5! = 5 × 4 × 3 × 2 × 1

### Step 5: Perform the multiplication
Calculating this step-by-step:
- 5 × 4 = 20
- 20 × 3 = 60
- 60 × 2 = 120
- 120 × 1 = 120

### Step 6: Conclusion
Thus, the number of ways 6 boys can form a ring is 120.

### Final Answer
The answer is 120.

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